a$.$ Construct a network diagram for a project consisting of the following activities:

b$.$ Suppose the project in a has the following activity times:

a$.$ Find the critical path.$($Use the CPM Method$)$

b$.$ What is the project completion time?

c$.$ Suppose the following estimates of activity times$($days$)$ are provided for in a:

a$.$ Determine the expected time and variance for the project.

b$.$ What is the probability that the project will be completed within $20$ days? $25$ days?